**Measurement of Inductance**

## AC Bridges

These bridges are used for the measurement of electrical quantities such as inductance, capacitance and resistance. AC bridges help us find out the storage factor, loss factor and dissipation factor when used in the circuits.

The circuit diagram of the AC bridge is similar to that of the DC bridge. The above AC bridge has four arms and each arm consists of some impedance. That means each arm will have either a single or combination of elements such as resistor, inductor and capacitor. Out of the four impedances two of them have a fixed value, the third one has a variable value and the fourth has an unknown value which can easily be measured using AC bridges.

## Hay’s Bridge

**Hay’s bridge** is a modification to a Wheatstone bridge used to measure inductance. It is quite similar to Maxwell’s bridge in components but the key difference lies in the connection pattern of both capacitors and inductors in the circuit. It is used to determine the inductance of an inductor with a high Q – factor. The working principle of Hay’s bridge is that the positive phase angle of an inductive impedance can be compensated by the negative phase angle of a capacitive impedance when put in the opposite arm and the circuit is at resonance; i.e., no potential difference across the detector and hence no current flows through it.

Here,

L_{X} = Unknown Inductance having a resistance R_{1}

R_{2} , R_{3} , R_{4} = Known resistance

C_{4} = Standard Capacitor

The balanced equation of each branch can be written as:

Equating the real and imaginary parts,

Solving the above two equations,

The quality factor of the coil Q,

There are two types of Hay bridges:

- Hay’s Inductance bridge where only inductors and resistors are used.
- Hay’s Inductance and Capacitance bridge where inductors, capacitors and resistors are used.

## Advantages of Hay’s Bridge

The balanced equations solve for simple value frequency factor and use small values of frequency factor.

## Disadvantages of Hay’s Bridge

The bridge is not suitable for the measurement of inductor coils having a quality factor value less than 10 (Q < 10).